How to slide and extrude
The trick is to use some supporting geometry. Rather than extruding, add a face and use the knife tool to make an additional edge:


If you use 'c' with the knife tool you'll get a perpendicular edge.
Now loop slide your new edge with 'C':


If you don't want to add and then remove faces, you can select the two edges that are adjacent to the edge you want to extend and subdivide them:

then use 'f' to connect the two new vertices:

and do the loop slide:

Also, start the edge slide with 'gg' and then move the edge slightly before entering 'C' so that Blender knows which direction you want to extend in.